Question

A number is increased by 30%and then decreased by 36%. Find the net increase decreased percent.

Answer 1

Answer:

Let the number be x.

When the number is increased by 30%,

Then the number will become;

=> x + 30% of x

=> x + (30/100)x

=> x + 3x/10

=> (10x + 3x)/10

=> 13x/10

Now,

When the new number obtained (after increasing it by 30%) is decreased by 36%, then the final number obtained;

=> 13x/10 - 36% of (13x/10)

=> (13x/10)(1 - 36%)

=> (13x/10)(1 - 36/100)

=> (13x/10)(64/100)

=> 13•64x/10•100

=> 832x/1000

%change = {(final - initial)•100/initial}%

Here,

Initial number = x

Final number = 832x/1000

Thus,

%change

= {(832x/1000 - x)•(100/x)}%

= {(832x/10 - 100x)/x}%

= (832/10 - 100)%

= (832/10 - 100)%

= {(832 - 1000)/10}%

= -168/10 %

= - 16.8 %

Here, the negative sign shows that, there is net decrease in the number.

Hence, there will be net decrease of 16.8% in the number.